I was wondering if the OSBDM/OSJTAG port on the tower modules of the Kinetis K series MCUs (TWR-K21D50M) can be used to program another target MCU from the Kinetis family. If yes, what is the process? Also can it be used for programming MCUs of the L series family as well?

The OSBDM/OSJTAG only supports JTAG communication. It will not work with devices that only support SWD debug communication protocol.

The OSBDM/OSJTAG designs are made to work with and validated against on-board target devices. While you might be able to get it to work with an external Kinetis device, this functionality is not validated by P&E or NXP and is not officially supported.